Many worlds interpretation with unequal probabilities

[PeterDonis]

A single particle whose wave function contains the reflected photon and the transmitted photon in equal proportions???? Quite ridiculous!

Huh? What's ridiculous about it?

 

[PeterDonis]

How does the many worlds interpretation deal with events where there are two possible outcomes with unequal probability. Or worse, when the probabiliy ratio is an irrational number?

I don't know if there is a unique answer to this among MWI proponents. Some view the relative weights of the branches as a "measure" of the worlds, others don't.

 

[PeterDonis]

There is, in any case, no uniquely identifiable state that corresponds to a dead cat. Nor to a live cat. To suppose there are only two states seems to invoke the "magic split" mentioned above.

No, it isn't. You don't need to have just two states. All you need is two orthogonal subspaces of the cat's Hilbert space. Each subspace could contain zillions of states, as long as all of the states in the "alive" subspace are orthogonal to all of the states in the "dead" subspace.

The real issue is whether what I have just described is actually feasible. Discussions of the Schrödinger's cat thought experiment seem to assume without argument that it is, but I don't think anyone has actually tried to prove it, or even to give a plausibility argument for it.

 

[kered rettop]

Huh? What's ridiculous about it?

I was being ironic, for goodness sake!

 

[kered rettop]

You are missing the point. The point is that this operator you speak of is a different operator if we apply it at different times. In the Heisenberg picture this is obvious. And if you are trying to count "worlds", you have to take that into account; you can't just say "well, the cat is either dead or alive", because different times of death for the cat are macroscopically distinguishable, so they count as different worlds.

You are not addressing this point at all.

You can sum the timed dead-cat worlds together to create a single timeless one so I'm not sure what the point is that you think I ought to address.

 

[PeroK]

I have to agree with @kered rettop 's analysis of the situation.

The article at https://plato.stanford.edu/entries/qm-manyworlds/ is a brilliant primer for anyone wanting to understand the MWI interpretation of QM. In particular, the section on the preferred basis problem talks about the partitioning of hilbert space into worlds in order to represent a quantum state.

Please describe, in QM terms, your proposed measurement to determine whether a cat is alive or dead?

Please describe how this act of measurement results in the cat being alive or dead. I.e. the appropriate eigenstate of your observable.

What if a test on a cat involved a biopsy - taking a small sample of the cat and processing it in a lab? Does that meet the criteria of a measurement in QM. Suppose you get the result back a day later. When was the cat measured - when the biopsy was taken, when the lab processed the sample or when you got the results?

PS if you take a biopsy, is it still the same cat that's left alive or dead?

 

[jbergman]

You are missing the point. The point is that this operator you speak of is a different operator if we apply it at different times. In the Heisenberg picture this is obvious. And if you are trying to count "worlds", you have to take that into account; you can't just say "well, the cat is either dead or alive", because different times of death for the cat are macroscopically distinguishable, so they count as different worlds.

You are not addressing this point at all.

I just wanted to say that understanding MWI in the Heisenberg picture is a nontrivial exercise. I've been meaning to get around to reading Kuyper and Deutsch's paper on it, https://arxiv.org/abs/2008.02328

 

[PeterDonis]

I was being ironic, for goodness sake!

That was not at all clear from your post. I would strongly suggest either avoiding irony or making it much clearer when you are doing it.

 

[PeterDonis]

You can sum the timed dead-cat worlds together to create a single timeless one

No, you can't. You can't "sum" worlds; they are macroscopically distinguishable and they can't interfere with each other.

This is not your thread and your posts are rapidly approaching the point where they are doing more harm than good to the OP's understanding. Please take heed.

 

[jbergman]

Please describe, in QM terms, your proposed measurement to determine whether a cat is alive or dead?

Please describe how this act of measurement results in the cat being alive or dead. I.e. the appropriate eigenstate of your observable.

What if a test on a cat involved a biopsy - taking a small sample of the cat and processing it in a lab? Does that meet the criteria of a measurement in QM. Suppose you get the result back a day later. When was the cat measured - when the biopsy was taken, when the lab processed the sample or when you got the results?

PS if you take a biopsy, is it still the same cat that's left alive or dead?

I will have to search the literature to answer this. I think this is an important question to get the right answer to.

 

[kered rettop]

No, you can't. You can't "sum" worlds; they are macroscopically distinguishable and they can't interfere with each other.

This needs discussing properly.

This is not your thread and your posts are rapidly approaching the point where they are doing more harm than good to the OP's understanding. Please take heed.

If you say so. I may start another thread to get the point clarified, if that's OK.

 

[PeterDonis]

This needs discussing properly.

If you can give a reference as a basis for your claim that "worlds" can be added, sure.

I may start another thread to get the point clarified, if that's OK.

Only if you have a valid reference.